LMFDB - Embedded newform 7098.2.a.ct.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.48406561.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 $ x^6 - 3x^5 - 17x^4 + 39x^3 + 111x^2 - 131*x - 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.41496$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.41496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} +1.00000 q^{18} -2.73858 q^{19} -2.41496 q^{20} +1.00000 q^{21} +3.24698 q^{22} -6.58012 q^{23} +1.00000 q^{24} +0.832022 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.22322 q^{29} -2.41496 q^{30} +2.72294 q^{31} +1.00000 q^{32} +3.24698 q^{33} +1.80194 q^{34} -2.41496 q^{35} +1.00000 q^{36} +8.93878 q^{37} -2.73858 q^{38} -2.41496 q^{40} +9.15862 q^{41} +1.00000 q^{42} -3.95322 q^{43} +3.24698 q^{44} -2.41496 q^{45} -6.58012 q^{46} +9.77289 q^{47} +1.00000 q^{48} +1.00000 q^{49} +0.832022 q^{50} +1.80194 q^{51} -10.3747 q^{53} +1.00000 q^{54} -7.84132 q^{55} +1.00000 q^{56} -2.73858 q^{57} +6.22322 q^{58} -4.50007 q^{59} -2.41496 q^{60} +6.94297 q^{61} +2.72294 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} -2.54486 q^{67} +1.80194 q^{68} -6.58012 q^{69} -2.41496 q^{70} -1.50961 q^{71} +1.00000 q^{72} -0.786291 q^{73} +8.93878 q^{74} +0.832022 q^{75} -2.73858 q^{76} +3.24698 q^{77} -2.41753 q^{79} -2.41496 q^{80} +1.00000 q^{81} +9.15862 q^{82} -3.51468 q^{83} +1.00000 q^{84} -4.35160 q^{85} -3.95322 q^{86} +6.22322 q^{87} +3.24698 q^{88} +10.9361 q^{89} -2.41496 q^{90} -6.58012 q^{92} +2.72294 q^{93} +9.77289 q^{94} +6.61356 q^{95} +1.00000 q^{96} +12.2904 q^{97} +1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.41496	−1.08000	−0.540001	−	0.841664i	$-0.681576\pi$
$5$	−2.41496	−1.08000	−0.540001	+	0.841664i	$0.681576\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.41496	−0.763677
$11$	3.24698	0.979001	0.489501	−	0.872003i	$-0.337179\pi$
$11$	3.24698	0.979001	0.489501	+	0.872003i	$0.337179\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−2.41496	−0.623539
$16$	1.00000	0.250000
$17$	1.80194	0.437034	0.218517	−	0.975833i	$-0.429878\pi$
$17$	1.80194	0.437034	0.218517	+	0.975833i	$0.429878\pi$
$18$	1.00000	0.235702
$19$	−2.73858	−0.628274	−0.314137	−	0.949378i	$-0.601715\pi$
$19$	−2.73858	−0.628274	−0.314137	+	0.949378i	$0.601715\pi$
$20$	−2.41496	−0.540001
$21$	1.00000	0.218218
$22$	3.24698	0.692258
$23$	−6.58012	−1.37205	−0.686025	−	0.727578i	$-0.740646\pi$
$23$	−6.58012	−1.37205	−0.686025	+	0.727578i	$0.740646\pi$
$24$	1.00000	0.204124
$25$	0.832022	0.166404
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	6.22322	1.15562	0.577812	−	0.816170i	$-0.303907\pi$
$29$	6.22322	1.15562	0.577812	+	0.816170i	$0.303907\pi$
$30$	−2.41496	−0.440909
$31$	2.72294	0.489054	0.244527	−	0.969643i	$-0.421367\pi$
$31$	2.72294	0.489054	0.244527	+	0.969643i	$0.421367\pi$
$32$	1.00000	0.176777
$33$	3.24698	0.565227
$34$	1.80194	0.309030
$35$	−2.41496	−0.408202
$36$	1.00000	0.166667
$37$	8.93878	1.46953	0.734764	−	0.678323i	$-0.237293\pi$
$37$	8.93878	1.46953	0.734764	+	0.678323i	$0.237293\pi$
$38$	−2.73858	−0.444257
$39$	0	0
$40$	−2.41496	−0.381838
$41$	9.15862	1.43034	0.715168	−	0.698953i	$-0.246350\pi$
$41$	9.15862	1.43034	0.715168	+	0.698953i	$0.246350\pi$
$42$	1.00000	0.154303
$43$	−3.95322	−0.602861	−0.301430	−	0.953488i	$-0.597464\pi$
$43$	−3.95322	−0.602861	−0.301430	+	0.953488i	$0.597464\pi$
$44$	3.24698	0.489501
$45$	−2.41496	−0.360001
$46$	−6.58012	−0.970186
$47$	9.77289	1.42552	0.712761	−	0.701407i	$-0.247444\pi$
$47$	9.77289	1.42552	0.712761	+	0.701407i	$0.247444\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	0.832022	0.117666
$51$	1.80194	0.252322
$52$	0	0
$53$	−10.3747	−1.42507	−0.712536	−	0.701636i	$-0.752453\pi$
$53$	−10.3747	−1.42507	−0.712536	+	0.701636i	$0.752453\pi$
$54$	1.00000	0.136083
$55$	−7.84132	−1.05732
$56$	1.00000	0.133631
$57$	−2.73858	−0.362734
$58$	6.22322	0.817149
$59$	−4.50007	−0.585859	−0.292930	−	0.956134i	$-0.594630\pi$
$59$	−4.50007	−0.585859	−0.292930	+	0.956134i	$0.594630\pi$
$60$	−2.41496	−0.311770
$61$	6.94297	0.888957	0.444478	−	0.895790i	$-0.353389\pi$
$61$	6.94297	0.888957	0.444478	+	0.895790i	$0.353389\pi$
$62$	2.72294	0.345813
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	3.24698	0.399676
$67$	−2.54486	−0.310904	−0.155452	−	0.987843i	$-0.549683\pi$
$67$	−2.54486	−0.310904	−0.155452	+	0.987843i	$0.549683\pi$
$68$	1.80194	0.218517
$69$	−6.58012	−0.792153
$70$	−2.41496	−0.288643
$71$	−1.50961	−0.179157	−0.0895787	−	0.995980i	$-0.528552\pi$
$71$	−1.50961	−0.179157	−0.0895787	+	0.995980i	$0.528552\pi$
$72$	1.00000	0.117851
$73$	−0.786291	−0.0920283	−0.0460142	−	0.998941i	$-0.514652\pi$
$73$	−0.786291	−0.0920283	−0.0460142	+	0.998941i	$0.514652\pi$
$74$	8.93878	1.03911
$75$	0.832022	0.0960736
$76$	−2.73858	−0.314137
$77$	3.24698	0.370028
$78$	0	0
$79$	−2.41753	−0.271993	−0.135997	−	0.990709i	$-0.543424\pi$
$79$	−2.41753	−0.271993	−0.135997	+	0.990709i	$0.543424\pi$
$80$	−2.41496	−0.270001
$81$	1.00000	0.111111
$82$	9.15862	1.01140
$83$	−3.51468	−0.385786	−0.192893	−	0.981220i	$-0.561787\pi$
$83$	−3.51468	−0.385786	−0.192893	+	0.981220i	$0.561787\pi$
$84$	1.00000	0.109109
$85$	−4.35160	−0.471998
$86$	−3.95322	−0.426287
$87$	6.22322	0.667200
$88$	3.24698	0.346129
$89$	10.9361	1.15922	0.579610	−	0.814894i	$-0.303205\pi$
$89$	10.9361	1.15922	0.579610	+	0.814894i	$0.303205\pi$
$90$	−2.41496	−0.254559
$91$	0	0
$92$	−6.58012	−0.686025
$93$	2.72294	0.282355
$94$	9.77289	1.00800
$95$	6.61356	0.678537
$96$	1.00000	0.102062
$97$	12.2904	1.24790	0.623950	−	0.781464i	$-0.285527\pi$
$97$	12.2904	1.24790	0.623950	+	0.781464i	$0.285527\pi$
$98$	1.00000	0.101015
$99$	3.24698	0.326334
$100$	0.832022	0.0832022
$101$	15.5746	1.54973	0.774866	−	0.632126i	$-0.217817\pi$
$101$	15.5746	1.54973	0.774866	+	0.632126i	$0.217817\pi$
$102$	1.80194	0.178418
$103$	3.71813	0.366358	0.183179	−	0.983080i	$-0.441361\pi$
$103$	3.71813	0.366358	0.183179	+	0.983080i	$0.441361\pi$
$104$	0	0
$105$	−2.41496	−0.235676
$106$	−10.3747	−1.00768
$107$	−0.125781	−0.0121597	−0.00607983	−	0.999982i	$-0.501935\pi$
$107$	−0.125781	−0.0121597	−0.00607983	+	0.999982i	$0.501935\pi$
$108$	1.00000	0.0962250
$109$	3.84276	0.368070	0.184035	−	0.982920i	$-0.441084\pi$
$109$	3.84276	0.368070	0.184035	+	0.982920i	$0.441084\pi$
$110$	−7.84132	−0.747640
$111$	8.93878	0.848432
$112$	1.00000	0.0944911
$113$	12.7648	1.20082	0.600408	−	0.799694i	$-0.295005\pi$
$113$	12.7648	1.20082	0.600408	+	0.799694i	$0.295005\pi$
$114$	−2.73858	−0.256492
$115$	15.8907	1.48182
$116$	6.22322	0.577812
$117$	0	0
$118$	−4.50007	−0.414265
$119$	1.80194	0.165183
$120$	−2.41496	−0.220454
$121$	−0.457123	−0.0415567
$122$	6.94297	0.628587
$123$	9.15862	0.825805
$124$	2.72294	0.244527
$125$	10.0655	0.900285
$126$	1.00000	0.0890871
$127$	−11.7970	−1.04682	−0.523408	−	0.852082i	$-0.675340\pi$
$127$	−11.7970	−1.04682	−0.523408	+	0.852082i	$0.675340\pi$
$128$	1.00000	0.0883883
$129$	−3.95322	−0.348062
$130$	0	0
$131$	−16.5193	−1.44330	−0.721649	−	0.692259i	$-0.756615\pi$
$131$	−16.5193	−1.44330	−0.721649	+	0.692259i	$0.756615\pi$
$132$	3.24698	0.282613
$133$	−2.73858	−0.237465
$134$	−2.54486	−0.219843
$135$	−2.41496	−0.207846
$136$	1.80194	0.154515
$137$	11.5650	0.988068	0.494034	−	0.869443i	$-0.335522\pi$
$137$	11.5650	0.988068	0.494034	+	0.869443i	$0.335522\pi$
$138$	−6.58012	−0.560137
$139$	−2.63433	−0.223441	−0.111720	−	0.993740i	$-0.535636\pi$
$139$	−2.63433	−0.223441	−0.111720	+	0.993740i	$0.535636\pi$
$140$	−2.41496	−0.204101
$141$	9.77289	0.823026
$142$	−1.50961	−0.126683
$143$	0	0
$144$	1.00000	0.0833333
$145$	−15.0288	−1.24808
$146$	−0.786291	−0.0650739
$147$	1.00000	0.0824786
$148$	8.93878	0.734764
$149$	−19.3553	−1.58565	−0.792825	−	0.609450i	$-0.791391\pi$
$149$	−19.3553	−1.58565	−0.792825	+	0.609450i	$0.791391\pi$
$150$	0.832022	0.0679343
$151$	9.50760	0.773717	0.386859	−	0.922139i	$-0.373560\pi$
$151$	9.50760	0.773717	0.386859	+	0.922139i	$0.373560\pi$
$152$	−2.73858	−0.222128
$153$	1.80194	0.145678
$154$	3.24698	0.261649
$155$	−6.57578	−0.528179
$156$	0	0
$157$	2.70530	0.215907	0.107953	−	0.994156i	$-0.465570\pi$
$157$	2.70530	0.215907	0.107953	+	0.994156i	$0.465570\pi$
$158$	−2.41753	−0.192328
$159$	−10.3747	−0.822766
$160$	−2.41496	−0.190919
$161$	−6.58012	−0.518586
$162$	1.00000	0.0785674
$163$	−6.79361	−0.532117	−0.266058	−	0.963957i	$-0.585721\pi$
$163$	−6.79361	−0.532117	−0.266058	+	0.963957i	$0.585721\pi$
$164$	9.15862	0.715168
$165$	−7.84132	−0.610446
$166$	−3.51468	−0.272792
$167$	17.9654	1.39020	0.695101	−	0.718912i	$-0.255360\pi$
$167$	17.9654	1.39020	0.695101	+	0.718912i	$0.255360\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−4.35160	−0.333753
$171$	−2.73858	−0.209425
$172$	−3.95322	−0.301430
$173$	−7.21332	−0.548418	−0.274209	−	0.961670i	$-0.588416\pi$
$173$	−7.21332	−0.548418	−0.274209	+	0.961670i	$0.588416\pi$
$174$	6.22322	0.471781
$175$	0.832022	0.0628949
$176$	3.24698	0.244750
$177$	−4.50007	−0.338246
$178$	10.9361	0.819693
$179$	3.27893	0.245079	0.122539	−	0.992464i	$-0.460896\pi$
$179$	3.27893	0.245079	0.122539	+	0.992464i	$0.460896\pi$
$180$	−2.41496	−0.180000
$181$	21.0091	1.56160	0.780798	−	0.624783i	$-0.214813\pi$
$181$	21.0091	1.56160	0.780798	+	0.624783i	$0.214813\pi$
$182$	0	0
$183$	6.94297	0.513239
$184$	−6.58012	−0.485093
$185$	−21.5868	−1.58709
$186$	2.72294	0.199655
$187$	5.85086	0.427857
$188$	9.77289	0.712761
$189$	1.00000	0.0727393
$190$	6.61356	0.479798
$191$	−6.15290	−0.445208	−0.222604	−	0.974909i	$-0.571456\pi$
$191$	−6.15290	−0.445208	−0.222604	+	0.974909i	$0.571456\pi$
$192$	1.00000	0.0721688
$193$	−18.6232	−1.34053	−0.670265	−	0.742122i	$-0.733819\pi$
$193$	−18.6232	−1.34053	−0.670265	+	0.742122i	$0.733819\pi$
$194$	12.2904	0.882398
$195$	0	0
$196$	1.00000	0.0714286
$197$	16.8553	1.20089	0.600443	−	0.799667i	$-0.294991\pi$
$197$	16.8553	1.20089	0.600443	+	0.799667i	$0.294991\pi$
$198$	3.24698	0.230753
$199$	12.3376	0.874589	0.437295	−	0.899318i	$-0.355937\pi$
$199$	12.3376	0.874589	0.437295	+	0.899318i	$0.355937\pi$
$200$	0.832022	0.0588328
$201$	−2.54486	−0.179501
$202$	15.5746	1.09583
$203$	6.22322	0.436785
$204$	1.80194	0.126161
$205$	−22.1177	−1.54477
$206$	3.71813	0.259055
$207$	−6.58012	−0.457350
$208$	0	0
$209$	−8.89213	−0.615081
$210$	−2.41496	−0.166648
$211$	−15.6160	−1.07505	−0.537525	−	0.843248i	$-0.680641\pi$
$211$	−15.6160	−1.07505	−0.537525	+	0.843248i	$0.680641\pi$
$212$	−10.3747	−0.712536
$213$	−1.50961	−0.103437
$214$	−0.125781	−0.00859818
$215$	9.54686	0.651091
$216$	1.00000	0.0680414
$217$	2.72294	0.184845
$218$	3.84276	0.260264
$219$	−0.786291	−0.0531326
$220$	−7.84132	−0.528662
$221$	0	0
$222$	8.93878	0.599932
$223$	5.53203	0.370452	0.185226	−	0.982696i	$-0.440698\pi$
$223$	5.53203	0.370452	0.185226	+	0.982696i	$0.440698\pi$
$224$	1.00000	0.0668153
$225$	0.832022	0.0554681
$226$	12.7648	0.849105
$227$	20.4532	1.35753	0.678763	−	0.734357i	$-0.262516\pi$
$227$	20.4532	1.35753	0.678763	+	0.734357i	$0.262516\pi$
$228$	−2.73858	−0.181367
$229$	−29.0317	−1.91847	−0.959234	−	0.282612i	$-0.908799\pi$
$229$	−29.0317	−1.91847	−0.959234	+	0.282612i	$0.908799\pi$
$230$	15.8907	1.04780
$231$	3.24698	0.213636
$232$	6.22322	0.408575
$233$	12.4742	0.817211	0.408605	−	0.912711i	$-0.366015\pi$
$233$	12.4742	0.817211	0.408605	+	0.912711i	$0.366015\pi$
$234$	0	0
$235$	−23.6011	−1.53957
$236$	−4.50007	−0.292930
$237$	−2.41753	−0.157035
$238$	1.80194	0.116802
$239$	−23.3225	−1.50861	−0.754303	−	0.656527i	$-0.772025\pi$
$239$	−23.3225	−1.50861	−0.754303	+	0.656527i	$0.772025\pi$
$240$	−2.41496	−0.155885
$241$	28.8105	1.85584	0.927922	−	0.372773i	$-0.121593\pi$
$241$	28.8105	1.85584	0.927922	+	0.372773i	$0.121593\pi$
$242$	−0.457123	−0.0293850
$243$	1.00000	0.0641500
$244$	6.94297	0.444478
$245$	−2.41496	−0.154286
$246$	9.15862	0.583932
$247$	0	0
$248$	2.72294	0.172907
$249$	−3.51468	−0.222734
$250$	10.0655	0.636598
$251$	1.56870	0.0990152	0.0495076	−	0.998774i	$-0.484235\pi$
$251$	1.56870	0.0990152	0.0495076	+	0.998774i	$0.484235\pi$
$252$	1.00000	0.0629941
$253$	−21.3655	−1.34324
$254$	−11.7970	−0.740211
$255$	−4.35160	−0.272508
$256$	1.00000	0.0625000
$257$	−14.0911	−0.878981	−0.439491	−	0.898247i	$-0.644841\pi$
$257$	−14.0911	−0.878981	−0.439491	+	0.898247i	$0.644841\pi$
$258$	−3.95322	−0.246117
$259$	8.93878	0.555429
$260$	0	0
$261$	6.22322	0.385208
$262$	−16.5193	−1.02057
$263$	−6.63837	−0.409339	−0.204670	−	0.978831i	$-0.565612\pi$
$263$	−6.63837	−0.409339	−0.204670	+	0.978831i	$0.565612\pi$
$264$	3.24698	0.199838
$265$	25.0544	1.53908
$266$	−2.73858	−0.167913
$267$	10.9361	0.669276
$268$	−2.54486	−0.155452
$269$	18.0426	1.10007	0.550037	−	0.835140i	$-0.314614\pi$
$269$	18.0426	1.10007	0.550037	+	0.835140i	$0.314614\pi$
$270$	−2.41496	−0.146970
$271$	12.0877	0.734277	0.367139	−	0.930166i	$-0.380337\pi$
$271$	12.0877	0.734277	0.367139	+	0.930166i	$0.380337\pi$
$272$	1.80194	0.109259
$273$	0	0
$274$	11.5650	0.698670
$275$	2.70156	0.162910
$276$	−6.58012	−0.396077
$277$	30.1936	1.81416	0.907080	−	0.420958i	$-0.138306\pi$
$277$	30.1936	1.81416	0.907080	+	0.420958i	$0.138306\pi$
$278$	−2.63433	−0.157997
$279$	2.72294	0.163018
$280$	−2.41496	−0.144321
$281$	20.4356	1.21909	0.609543	−	0.792753i	$-0.291353\pi$
$281$	20.4356	1.21909	0.609543	+	0.792753i	$0.291353\pi$
$282$	9.77289	0.581967
$283$	−4.01876	−0.238890	−0.119445	−	0.992841i	$-0.538112\pi$
$283$	−4.01876	−0.238890	−0.119445	+	0.992841i	$0.538112\pi$
$284$	−1.50961	−0.0895787
$285$	6.61356	0.391754
$286$	0	0
$287$	9.15862	0.540616
$288$	1.00000	0.0589256
$289$	−13.7530	−0.809001
$290$	−15.0288	−0.882523
$291$	12.2904	0.720475
$292$	−0.786291	−0.0460142
$293$	19.3490	1.13038	0.565191	−	0.824960i	$-0.308802\pi$
$293$	19.3490	1.13038	0.565191	+	0.824960i	$0.308802\pi$
$294$	1.00000	0.0583212
$295$	10.8675	0.632729
$296$	8.93878	0.519556
$297$	3.24698	0.188409
$298$	−19.3553	−1.12122
$299$	0	0
$300$	0.832022	0.0480368
$301$	−3.95322	−0.227860
$302$	9.50760	0.547101
$303$	15.5746	0.894738
$304$	−2.73858	−0.157069
$305$	−16.7670	−0.960075
$306$	1.80194	0.103010
$307$	5.04050	0.287677	0.143838	−	0.989601i	$-0.454055\pi$
$307$	5.04050	0.287677	0.143838	+	0.989601i	$0.454055\pi$
$308$	3.24698	0.185014
$309$	3.71813	0.211517
$310$	−6.57578	−0.373479
$311$	−16.2638	−0.922235	−0.461117	−	0.887339i	$-0.652551\pi$
$311$	−16.2638	−0.922235	−0.461117	+	0.887339i	$0.652551\pi$
$312$	0	0
$313$	−8.80560	−0.497722	−0.248861	−	0.968539i	$-0.580056\pi$
$313$	−8.80560	−0.497722	−0.248861	+	0.968539i	$0.580056\pi$
$314$	2.70530	0.152669
$315$	−2.41496	−0.136067
$316$	−2.41753	−0.135997
$317$	20.0495	1.12609	0.563047	−	0.826425i	$-0.309629\pi$
$317$	20.0495	1.12609	0.563047	+	0.826425i	$0.309629\pi$
$318$	−10.3747	−0.581783
$319$	20.2067	1.13136
$320$	−2.41496	−0.135000
$321$	−0.125781	−0.00702039
$322$	−6.58012	−0.366696
$323$	−4.93476	−0.274577
$324$	1.00000	0.0555556
$325$	0	0
$326$	−6.79361	−0.376263
$327$	3.84276	0.212505
$328$	9.15862	0.505700
$329$	9.77289	0.538797
$330$	−7.84132	−0.431650
$331$	−19.0732	−1.04836	−0.524180	−	0.851607i	$-0.675628\pi$
$331$	−19.0732	−1.04836	−0.524180	+	0.851607i	$0.675628\pi$
$332$	−3.51468	−0.192893
$333$	8.93878	0.489842
$334$	17.9654	0.983021
$335$	6.14573	0.335777
$336$	1.00000	0.0545545
$337$	14.8542	0.809159	0.404580	−	0.914503i	$-0.367418\pi$
$337$	14.8542	0.809159	0.404580	+	0.914503i	$0.367418\pi$
$338$	0	0
$339$	12.7648	0.693291
$340$	−4.35160	−0.235999
$341$	8.84132	0.478784
$342$	−2.73858	−0.148086
$343$	1.00000	0.0539949
$344$	−3.95322	−0.213143
$345$	15.8907	0.855527
$346$	−7.21332	−0.387790
$347$	26.6896	1.43277	0.716386	−	0.697704i	$-0.245795\pi$
$347$	26.6896	1.43277	0.716386	+	0.697704i	$0.245795\pi$
$348$	6.22322	0.333600
$349$	−31.8560	−1.70521	−0.852607	−	0.522552i	$-0.824980\pi$
$349$	−31.8560	−1.70521	−0.852607	+	0.522552i	$0.824980\pi$
$350$	0.832022	0.0444734
$351$	0	0
$352$	3.24698	0.173065
$353$	−3.52242	−0.187480	−0.0937398	−	0.995597i	$-0.529882\pi$
$353$	−3.52242	−0.187480	−0.0937398	+	0.995597i	$0.529882\pi$
$354$	−4.50007	−0.239176
$355$	3.64564	0.193490
$356$	10.9361	0.579610
$357$	1.80194	0.0953687
$358$	3.27893	0.173297
$359$	24.0153	1.26748	0.633740	−	0.773546i	$-0.281519\pi$
$359$	24.0153	1.26748	0.633740	+	0.773546i	$0.281519\pi$
$360$	−2.41496	−0.127279
$361$	−11.5002	−0.605272
$362$	21.0091	1.10422
$363$	−0.457123	−0.0239928
$364$	0	0
$365$	1.89886	0.0993908
$366$	6.94297	0.362915
$367$	−5.01103	−0.261574	−0.130787	−	0.991411i	$-0.541750\pi$
$367$	−5.01103	−0.261574	−0.130787	+	0.991411i	$0.541750\pi$
$368$	−6.58012	−0.343012
$369$	9.15862	0.476779
$370$	−21.5868	−1.12224
$371$	−10.3747	−0.538627
$372$	2.72294	0.141178
$373$	−12.2463	−0.634092	−0.317046	−	0.948410i	$-0.602691\pi$
$373$	−12.2463	−0.634092	−0.317046	+	0.948410i	$0.602691\pi$
$374$	5.85086	0.302541
$375$	10.0655	0.519780
$376$	9.77289	0.503998
$377$	0	0
$378$	1.00000	0.0514344
$379$	−15.3669	−0.789343	−0.394672	−	0.918822i	$-0.629142\pi$
$379$	−15.3669	−0.789343	−0.394672	+	0.918822i	$0.629142\pi$
$380$	6.61356	0.339269
$381$	−11.7970	−0.604379
$382$	−6.15290	−0.314810
$383$	13.7125	0.700675	0.350338	−	0.936623i	$-0.386067\pi$
$383$	13.7125	0.700675	0.350338	+	0.936623i	$0.386067\pi$
$384$	1.00000	0.0510310
$385$	−7.84132	−0.399631
$386$	−18.6232	−0.947897
$387$	−3.95322	−0.200954
$388$	12.2904	0.623950
$389$	9.05551	0.459133	0.229566	−	0.973293i	$-0.426269\pi$
$389$	9.05551	0.459133	0.229566	+	0.973293i	$0.426269\pi$
$390$	0	0
$391$	−11.8570	−0.599633
$392$	1.00000	0.0505076
$393$	−16.5193	−0.833288
$394$	16.8553	0.849155
$395$	5.83823	0.293753
$396$	3.24698	0.163167
$397$	−20.8502	−1.04644	−0.523220	−	0.852198i	$-0.675269\pi$
$397$	−20.8502	−1.04644	−0.523220	+	0.852198i	$0.675269\pi$
$398$	12.3376	0.618428
$399$	−2.73858	−0.137101
$400$	0.832022	0.0416011
$401$	−19.6443	−0.980988	−0.490494	−	0.871445i	$-0.663184\pi$
$401$	−19.6443	−0.980988	−0.490494	+	0.871445i	$0.663184\pi$
$402$	−2.54486	−0.126926
$403$	0	0
$404$	15.5746	0.774866
$405$	−2.41496	−0.120000
$406$	6.22322	0.308853
$407$	29.0240	1.43867
$408$	1.80194	0.0892092
$409$	−2.96748	−0.146733	−0.0733663	−	0.997305i	$-0.523374\pi$
$409$	−2.96748	−0.146733	−0.0733663	+	0.997305i	$0.523374\pi$
$410$	−22.1177	−1.09231
$411$	11.5650	0.570461
$412$	3.71813	0.183179
$413$	−4.50007	−0.221434
$414$	−6.58012	−0.323395
$415$	8.48781	0.416650
$416$	0	0
$417$	−2.63433	−0.129004
$418$	−8.89213	−0.434928
$419$	−0.255356	−0.0124750	−0.00623748	−	0.999981i	$-0.501985\pi$
$419$	−0.255356	−0.0124750	−0.00623748	+	0.999981i	$0.501985\pi$
$420$	−2.41496	−0.117838
$421$	−36.2298	−1.76573	−0.882867	−	0.469623i	$-0.844390\pi$
$421$	−36.2298	−1.76573	−0.882867	+	0.469623i	$0.844390\pi$
$422$	−15.6160	−0.760176
$423$	9.77289	0.475174
$424$	−10.3747	−0.503839
$425$	1.49925	0.0727244
$426$	−1.50961	−0.0731407
$427$	6.94297	0.335994
$428$	−0.125781	−0.00607983
$429$	0	0
$430$	9.54686	0.460391
$431$	26.6462	1.28350	0.641752	−	0.766913i	$-0.278208\pi$
$431$	26.6462	1.28350	0.641752	+	0.766913i	$0.278208\pi$
$432$	1.00000	0.0481125
$433$	−30.6061	−1.47083	−0.735417	−	0.677615i	$-0.763014\pi$
$433$	−30.6061	−1.47083	−0.735417	+	0.677615i	$0.763014\pi$
$434$	2.72294	0.130705
$435$	−15.0288	−0.720577
$436$	3.84276	0.184035
$437$	18.0202	0.862023
$438$	−0.786291	−0.0375704
$439$	−11.4091	−0.544525	−0.272262	−	0.962223i	$-0.587772\pi$
$439$	−11.4091	−0.544525	−0.272262	+	0.962223i	$0.587772\pi$
$440$	−7.84132	−0.373820
$441$	1.00000	0.0476190
$442$	0	0
$443$	38.5387	1.83103	0.915515	−	0.402283i	$-0.131783\pi$
$443$	38.5387	1.83103	0.915515	+	0.402283i	$0.131783\pi$
$444$	8.93878	0.424216
$445$	−26.4101	−1.25196
$446$	5.53203	0.261949
$447$	−19.3553	−0.915475
$448$	1.00000	0.0472456
$449$	−2.16519	−0.102182	−0.0510908	−	0.998694i	$-0.516270\pi$
$449$	−2.16519	−0.102182	−0.0510908	+	0.998694i	$0.516270\pi$
$450$	0.832022	0.0392219
$451$	29.7378	1.40030
$452$	12.7648	0.600408
$453$	9.50760	0.446706
$454$	20.4532	0.959917
$455$	0	0
$456$	−2.73858	−0.128246
$457$	−31.4845	−1.47278	−0.736392	−	0.676555i	$-0.763472\pi$
$457$	−31.4845	−1.47278	−0.736392	+	0.676555i	$0.763472\pi$
$458$	−29.0317	−1.35656
$459$	1.80194	0.0841073
$460$	15.8907	0.740908
$461$	7.94726	0.370141	0.185070	−	0.982725i	$-0.440749\pi$
$461$	7.94726	0.370141	0.185070	+	0.982725i	$0.440749\pi$
$462$	3.24698	0.151063
$463$	12.1131	0.562943	0.281471	−	0.959570i	$-0.409178\pi$
$463$	12.1131	0.562943	0.281471	+	0.959570i	$0.409178\pi$
$464$	6.22322	0.288906
$465$	−6.57578	−0.304944
$466$	12.4742	0.577855
$467$	−1.69520	−0.0784446	−0.0392223	−	0.999231i	$-0.512488\pi$
$467$	−1.69520	−0.0784446	−0.0392223	+	0.999231i	$0.512488\pi$
$468$	0	0
$469$	−2.54486	−0.117511
$470$	−23.6011	−1.08864
$471$	2.70530	0.124654
$472$	−4.50007	−0.207133
$473$	−12.8360	−0.590201
$474$	−2.41753	−0.111041
$475$	−2.27856	−0.104548
$476$	1.80194	0.0825917
$477$	−10.3747	−0.475024
$478$	−23.3225	−1.06675
$479$	3.59340	0.164187	0.0820933	−	0.996625i	$-0.473839\pi$
$479$	3.59340	0.164187	0.0820933	+	0.996625i	$0.473839\pi$
$480$	−2.41496	−0.110227
$481$	0	0
$482$	28.8105	1.31228
$483$	−6.58012	−0.299406
$484$	−0.457123	−0.0207783
$485$	−29.6808	−1.34773
$486$	1.00000	0.0453609
$487$	−4.79109	−0.217105	−0.108552	−	0.994091i	$-0.534622\pi$
$487$	−4.79109	−0.217105	−0.108552	+	0.994091i	$0.534622\pi$
$488$	6.94297	0.314294
$489$	−6.79361	−0.307218
$490$	−2.41496	−0.109097
$491$	−42.3139	−1.90960	−0.954800	−	0.297250i	$-0.903931\pi$
$491$	−42.3139	−1.90960	−0.954800	+	0.297250i	$0.903931\pi$
$492$	9.15862	0.412902
$493$	11.2139	0.505047
$494$	0	0
$495$	−7.84132	−0.352441
$496$	2.72294	0.122263
$497$	−1.50961	−0.0677151
$498$	−3.51468	−0.157497
$499$	26.4820	1.18550	0.592749	−	0.805387i	$-0.298042\pi$
$499$	26.4820	1.18550	0.592749	+	0.805387i	$0.298042\pi$
$500$	10.0655	0.450142
$501$	17.9654	0.802633
$502$	1.56870	0.0700143
$503$	16.9580	0.756121	0.378060	−	0.925781i	$-0.376591\pi$
$503$	16.9580	0.756121	0.378060	+	0.925781i	$0.376591\pi$
$504$	1.00000	0.0445435
$505$	−37.6120	−1.67371
$506$	−21.3655	−0.949813
$507$	0	0
$508$	−11.7970	−0.523408
$509$	−3.29901	−0.146226	−0.0731129	−	0.997324i	$-0.523293\pi$
$509$	−3.29901	−0.146226	−0.0731129	+	0.997324i	$0.523293\pi$
$510$	−4.35160	−0.192692
$511$	−0.786291	−0.0347834
$512$	1.00000	0.0441942
$513$	−2.73858	−0.120911
$514$	−14.0911	−0.621534
$515$	−8.97913	−0.395668
$516$	−3.95322	−0.174031
$517$	31.7324	1.39559
$518$	8.93878	0.392748
$519$	−7.21332	−0.316630
$520$	0	0
$521$	−3.85188	−0.168754	−0.0843770	−	0.996434i	$-0.526890\pi$
$521$	−3.85188	−0.168754	−0.0843770	+	0.996434i	$0.526890\pi$
$522$	6.22322	0.272383
$523$	−13.8862	−0.607201	−0.303601	−	0.952799i	$-0.598189\pi$
$523$	−13.8862	−0.607201	−0.303601	+	0.952799i	$0.598189\pi$
$524$	−16.5193	−0.721649
$525$	0.832022	0.0363124
$526$	−6.63837	−0.289447
$527$	4.90656	0.213733
$528$	3.24698	0.141307
$529$	20.2980	0.882521
$530$	25.0544	1.08829
$531$	−4.50007	−0.195286
$532$	−2.73858	−0.118733
$533$	0	0
$534$	10.9361	0.473250
$535$	0.303755	0.0131325
$536$	−2.54486	−0.109921
$537$	3.27893	0.141496
$538$	18.0426	0.777870
$539$	3.24698	0.139857
$540$	−2.41496	−0.103923
$541$	5.36925	0.230842	0.115421	−	0.993317i	$-0.463178\pi$
$541$	5.36925	0.230842	0.115421	+	0.993317i	$0.463178\pi$
$542$	12.0877	0.519212
$543$	21.0091	0.901588
$544$	1.80194	0.0772574
$545$	−9.28010	−0.397516
$546$	0	0
$547$	−46.0980	−1.97101	−0.985504	−	0.169653i	$-0.945735\pi$
$547$	−46.0980	−1.97101	−0.985504	+	0.169653i	$0.945735\pi$
$548$	11.5650	0.494034
$549$	6.94297	0.296319
$550$	2.70156	0.115195
$551$	−17.0428	−0.726049
$552$	−6.58012	−0.280068
$553$	−2.41753	−0.102804
$554$	30.1936	1.28281
$555$	−21.5868	−0.916308
$556$	−2.63433	−0.111720
$557$	15.3154	0.648936	0.324468	−	0.945897i	$-0.394815\pi$
$557$	15.3154	0.648936	0.324468	+	0.945897i	$0.394815\pi$
$558$	2.72294	0.115271
$559$	0	0
$560$	−2.41496	−0.102051
$561$	5.85086	0.247023
$562$	20.4356	0.862023
$563$	−8.13781	−0.342968	−0.171484	−	0.985187i	$-0.554856\pi$
$563$	−8.13781	−0.342968	−0.171484	+	0.985187i	$0.554856\pi$
$564$	9.77289	0.411513
$565$	−30.8266	−1.29688
$566$	−4.01876	−0.168921
$567$	1.00000	0.0419961
$568$	−1.50961	−0.0633417
$569$	−15.9128	−0.667099	−0.333550	−	0.942733i	$-0.608246\pi$
$569$	−15.9128	−0.667099	−0.333550	+	0.942733i	$0.608246\pi$
$570$	6.61356	0.277012
$571$	29.3918	1.23001	0.615004	−	0.788524i	$-0.289154\pi$
$571$	29.3918	1.23001	0.615004	+	0.788524i	$0.289154\pi$
$572$	0	0
$573$	−6.15290	−0.257041
$574$	9.15862	0.382273
$575$	−5.47480	−0.228315
$576$	1.00000	0.0416667
$577$	−22.0602	−0.918377	−0.459188	−	0.888339i	$-0.651860\pi$
$577$	−22.0602	−0.918377	−0.459188	+	0.888339i	$0.651860\pi$
$578$	−13.7530	−0.572050
$579$	−18.6232	−0.773955
$580$	−15.0288	−0.624038
$581$	−3.51468	−0.145814
$582$	12.2904	0.509453
$583$	−33.6864	−1.39515
$584$	−0.786291	−0.0325369
$585$	0	0
$586$	19.3490	0.799301
$587$	42.3330	1.74727	0.873634	−	0.486583i	$-0.161757\pi$
$587$	42.3330	1.74727	0.873634	+	0.486583i	$0.161757\pi$
$588$	1.00000	0.0412393
$589$	−7.45699	−0.307260
$590$	10.8675	0.447407
$591$	16.8553	0.693332
$592$	8.93878	0.367382
$593$	−13.0257	−0.534903	−0.267451	−	0.963571i	$-0.586182\pi$
$593$	−13.0257	−0.534903	−0.267451	+	0.963571i	$0.586182\pi$
$594$	3.24698	0.133225
$595$	−4.35160	−0.178398
$596$	−19.3553	−0.792825
$597$	12.3376	0.504944
$598$	0	0
$599$	−28.1604	−1.15060	−0.575301	−	0.817941i	$-0.695115\pi$
$599$	−28.1604	−1.15060	−0.575301	+	0.817941i	$0.695115\pi$
$600$	0.832022	0.0339671
$601$	26.9245	1.09827	0.549136	−	0.835733i	$-0.314957\pi$
$601$	26.9245	1.09827	0.549136	+	0.835733i	$0.314957\pi$
$602$	−3.95322	−0.161121
$603$	−2.54486	−0.103635
$604$	9.50760	0.386859
$605$	1.10393	0.0448813
$606$	15.5746	0.632675
$607$	19.1584	0.777617	0.388808	−	0.921319i	$-0.372887\pi$
$607$	19.1584	0.777617	0.388808	+	0.921319i	$0.372887\pi$
$608$	−2.73858	−0.111064
$609$	6.22322	0.252178
$610$	−16.7670	−0.678876
$611$	0	0
$612$	1.80194	0.0728390
$613$	−3.78753	−0.152977	−0.0764884	−	0.997070i	$-0.524371\pi$
$613$	−3.78753	−0.152977	−0.0764884	+	0.997070i	$0.524371\pi$
$614$	5.04050	0.203418
$615$	−22.1177	−0.891871
$616$	3.24698	0.130825
$617$	−24.0329	−0.967527	−0.483764	−	0.875199i	$-0.660731\pi$
$617$	−24.0329	−0.967527	−0.483764	+	0.875199i	$0.660731\pi$
$618$	3.71813	0.149565
$619$	−44.5020	−1.78869	−0.894344	−	0.447381i	$-0.852357\pi$
$619$	−44.5020	−1.78869	−0.894344	+	0.447381i	$0.852357\pi$
$620$	−6.57578	−0.264090
$621$	−6.58012	−0.264051
$622$	−16.2638	−0.652118
$623$	10.9361	0.438144
$624$	0	0
$625$	−28.4678	−1.13871
$626$	−8.80560	−0.351943
$627$	−8.89213	−0.355117
$628$	2.70530	0.107953
$629$	16.1071	0.642233
$630$	−2.41496	−0.0962142
$631$	−26.0186	−1.03579	−0.517893	−	0.855446i	$-0.673283\pi$
$631$	−26.0186	−1.03579	−0.517893	+	0.855446i	$0.673283\pi$
$632$	−2.41753	−0.0961642
$633$	−15.6160	−0.620681
$634$	20.0495	0.796269
$635$	28.4893	1.13056
$636$	−10.3747	−0.411383
$637$	0	0
$638$	20.2067	0.799990
$639$	−1.50961	−0.0597191
$640$	−2.41496	−0.0954596
$641$	−37.8504	−1.49500	−0.747500	−	0.664261i	$-0.768746\pi$
$641$	−37.8504	−1.49500	−0.747500	+	0.664261i	$0.768746\pi$
$642$	−0.125781	−0.00496416
$643$	26.4910	1.04470	0.522351	−	0.852731i	$-0.325055\pi$
$643$	26.4910	1.04470	0.522351	+	0.852731i	$0.325055\pi$
$644$	−6.58012	−0.259293
$645$	9.54686	0.375907
$646$	−4.93476	−0.194155
$647$	−34.8792	−1.37124	−0.685621	−	0.727959i	$-0.740469\pi$
$647$	−34.8792	−1.37124	−0.685621	+	0.727959i	$0.740469\pi$
$648$	1.00000	0.0392837
$649$	−14.6116	−0.573557
$650$	0	0
$651$	2.72294	0.106720
$652$	−6.79361	−0.266058
$653$	0.351211	0.0137439	0.00687197	−	0.999976i	$-0.497813\pi$
$653$	0.351211	0.0137439	0.00687197	+	0.999976i	$0.497813\pi$
$654$	3.84276	0.150264
$655$	39.8934	1.55876
$656$	9.15862	0.357584
$657$	−0.786291	−0.0306761
$658$	9.77289	0.380987
$659$	10.6161	0.413545	0.206773	−	0.978389i	$-0.433704\pi$
$659$	10.6161	0.413545	0.206773	+	0.978389i	$0.433704\pi$
$660$	−7.84132	−0.305223
$661$	−45.2269	−1.75912	−0.879561	−	0.475786i	$-0.842164\pi$
$661$	−45.2269	−1.75912	−0.879561	+	0.475786i	$0.842164\pi$
$662$	−19.0732	−0.741303
$663$	0	0
$664$	−3.51468	−0.136396
$665$	6.61356	0.256463
$666$	8.93878	0.346371
$667$	−40.9496	−1.58557
$668$	17.9654	0.695101
$669$	5.53203	0.213881
$670$	6.14573	0.237430
$671$	22.5437	0.870290
$672$	1.00000	0.0385758
$673$	16.2910	0.627973	0.313986	−	0.949428i	$-0.398335\pi$
$673$	16.2910	0.627973	0.313986	+	0.949428i	$0.398335\pi$
$674$	14.8542	0.572162
$675$	0.832022	0.0320245
$676$	0	0
$677$	−29.8672	−1.14789	−0.573946	−	0.818893i	$-0.694588\pi$
$677$	−29.8672	−1.14789	−0.573946	+	0.818893i	$0.694588\pi$
$678$	12.7648	0.490231
$679$	12.2904	0.471662
$680$	−4.35160	−0.166876
$681$	20.4532	0.783769
$682$	8.84132	0.338552
$683$	−3.26490	−0.124928	−0.0624640	−	0.998047i	$-0.519896\pi$
$683$	−3.26490	−0.124928	−0.0624640	+	0.998047i	$0.519896\pi$
$684$	−2.73858	−0.104712
$685$	−27.9291	−1.06712
$686$	1.00000	0.0381802
$687$	−29.0317	−1.10763
$688$	−3.95322	−0.150715
$689$	0	0
$690$	15.8907	0.604949
$691$	38.2216	1.45402	0.727010	−	0.686627i	$-0.240910\pi$
$691$	38.2216	1.45402	0.727010	+	0.686627i	$0.240910\pi$
$692$	−7.21332	−0.274209
$693$	3.24698	0.123343
$694$	26.6896	1.01312
$695$	6.36179	0.241317
$696$	6.22322	0.235891
$697$	16.5033	0.625105
$698$	−31.8560	−1.20577
$699$	12.4742	0.471817
$700$	0.832022	0.0314475
$701$	−16.1383	−0.609535	−0.304767	−	0.952427i	$-0.598579\pi$
$701$	−16.1383	−0.609535	−0.304767	+	0.952427i	$0.598579\pi$
$702$	0	0
$703$	−24.4796	−0.923266
$704$	3.24698	0.122375
$705$	−23.6011	−0.888870
$706$	−3.52242	−0.132568
$707$	15.5746	0.585744
$708$	−4.50007	−0.169123
$709$	17.2856	0.649176	0.324588	−	0.945856i	$-0.394774\pi$
$709$	17.2856	0.649176	0.324588	+	0.945856i	$0.394774\pi$
$710$	3.64564	0.136818
$711$	−2.41753	−0.0906645
$712$	10.9361	0.409846
$713$	−17.9172	−0.671006
$714$	1.80194	0.0674358
$715$	0	0
$716$	3.27893	0.122539
$717$	−23.3225	−0.870994
$718$	24.0153	0.896244
$719$	−32.0469	−1.19515	−0.597574	−	0.801814i	$-0.703868\pi$
$719$	−32.0469	−1.19515	−0.597574	+	0.801814i	$0.703868\pi$
$720$	−2.41496	−0.0900002
$721$	3.71813	0.138470
$722$	−11.5002	−0.427992
$723$	28.8105	1.07147
$724$	21.0091	0.780798
$725$	5.17786	0.192301
$726$	−0.457123	−0.0169654
$727$	−9.14186	−0.339053	−0.169526	−	0.985526i	$-0.554224\pi$
$727$	−9.14186	−0.339053	−0.169526	+	0.985526i	$0.554224\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.89886	0.0702799
$731$	−7.12346	−0.263471
$732$	6.94297	0.256620
$733$	−0.298008	−0.0110072	−0.00550359	−	0.999985i	$-0.501752\pi$
$733$	−0.298008	−0.0110072	−0.00550359	+	0.999985i	$0.501752\pi$
$734$	−5.01103	−0.184961
$735$	−2.41496	−0.0890771
$736$	−6.58012	−0.242546
$737$	−8.26311	−0.304376
$738$	9.15862	0.337133
$739$	−20.7127	−0.761931	−0.380965	−	0.924589i	$-0.624408\pi$
$739$	−20.7127	−0.761931	−0.380965	+	0.924589i	$0.624408\pi$
$740$	−21.5868	−0.793546
$741$	0	0
$742$	−10.3747	−0.380867
$743$	−43.7005	−1.60322	−0.801608	−	0.597849i	$-0.796022\pi$
$743$	−43.7005	−1.60322	−0.801608	+	0.597849i	$0.796022\pi$
$744$	2.72294	0.0998277
$745$	46.7423	1.71250
$746$	−12.2463	−0.448371
$747$	−3.51468	−0.128595
$748$	5.85086	0.213928
$749$	−0.125781	−0.00459592
$750$	10.0655	0.367540
$751$	−51.8962	−1.89372	−0.946860	−	0.321646i	$-0.895764\pi$
$751$	−51.8962	−1.89372	−0.946860	+	0.321646i	$0.895764\pi$
$752$	9.77289	0.356381
$753$	1.56870	0.0571664
$754$	0	0
$755$	−22.9604	−0.835616
$756$	1.00000	0.0363696
$757$	47.3170	1.71977	0.859883	−	0.510491i	$-0.170536\pi$
$757$	47.3170	1.71977	0.859883	+	0.510491i	$0.170536\pi$
$758$	−15.3669	−0.558150
$759$	−21.3655	−0.775519
$760$	6.61356	0.239899
$761$	13.5638	0.491687	0.245844	−	0.969310i	$-0.420935\pi$
$761$	13.5638	0.491687	0.245844	+	0.969310i	$0.420935\pi$
$762$	−11.7970	−0.427361
$763$	3.84276	0.139117
$764$	−6.15290	−0.222604
$765$	−4.35160	−0.157333
$766$	13.7125	0.495452
$767$	0	0
$768$	1.00000	0.0360844
$769$	−32.6689	−1.17807	−0.589036	−	0.808107i	$-0.700492\pi$
$769$	−32.6689	−1.17807	−0.589036	+	0.808107i	$0.700492\pi$
$770$	−7.84132	−0.282582
$771$	−14.0911	−0.507480
$772$	−18.6232	−0.670265
$773$	31.1438	1.12016	0.560082	−	0.828437i	$-0.310770\pi$
$773$	31.1438	1.12016	0.560082	+	0.828437i	$0.310770\pi$
$774$	−3.95322	−0.142096
$775$	2.26554	0.0813807
$776$	12.2904	0.441199
$777$	8.93878	0.320677
$778$	9.05551	0.324656
$779$	−25.0816	−0.898643
$780$	0	0
$781$	−4.90166	−0.175395
$782$	−11.8570	−0.424004
$783$	6.22322	0.222400
$784$	1.00000	0.0357143
$785$	−6.53320	−0.233180
$786$	−16.5193	−0.589224
$787$	−32.0019	−1.14075	−0.570373	−	0.821386i	$-0.693201\pi$
$787$	−32.0019	−1.14075	−0.570373	+	0.821386i	$0.693201\pi$
$788$	16.8553	0.600443
$789$	−6.63837	−0.236332
$790$	5.83823	0.207715
$791$	12.7648	0.453866
$792$	3.24698	0.115376
$793$	0	0
$794$	−20.8502	−0.739944
$795$	25.0544	0.888589
$796$	12.3376	0.437295
$797$	−23.5034	−0.832532	−0.416266	−	0.909243i	$-0.636661\pi$
$797$	−23.5034	−0.832532	−0.416266	+	0.909243i	$0.636661\pi$
$798$	−2.73858	−0.0969448
$799$	17.6101	0.623002
$800$	0.832022	0.0294164
$801$	10.9361	0.386407
$802$	−19.6443	−0.693663
$803$	−2.55307	−0.0900959
$804$	−2.54486	−0.0897504
$805$	15.8907	0.560074
$806$	0	0
$807$	18.0426	0.635128
$808$	15.5746	0.547913
$809$	0.626708	0.0220339	0.0110169	−	0.999939i	$-0.496493\pi$
$809$	0.626708	0.0220339	0.0110169	+	0.999939i	$0.496493\pi$
$810$	−2.41496	−0.0848530
$811$	−2.31714	−0.0813656	−0.0406828	−	0.999172i	$-0.512953\pi$
$811$	−2.31714	−0.0813656	−0.0406828	+	0.999172i	$0.512953\pi$
$812$	6.22322	0.218392
$813$	12.0877	0.423935
$814$	29.0240	1.01729
$815$	16.4063	0.574687
$816$	1.80194	0.0630804
$817$	10.8262	0.378762
$818$	−2.96748	−0.103756
$819$	0	0
$820$	−22.1177	−0.772383
$821$	45.6066	1.59168	0.795841	−	0.605505i	$-0.207029\pi$
$821$	45.6066	1.59168	0.795841	+	0.605505i	$0.207029\pi$
$822$	11.5650	0.403377
$823$	54.7826	1.90960	0.954801	−	0.297246i	$-0.0960680\pi$
$823$	54.7826	1.90960	0.954801	+	0.297246i	$0.0960680\pi$
$824$	3.71813	0.129527
$825$	2.70156	0.0940562
$826$	−4.50007	−0.156577
$827$	5.65372	0.196599	0.0982995	−	0.995157i	$-0.468660\pi$
$827$	5.65372	0.196599	0.0982995	+	0.995157i	$0.468660\pi$
$828$	−6.58012	−0.228675
$829$	−8.87143	−0.308117	−0.154059	−	0.988062i	$-0.549235\pi$
$829$	−8.87143	−0.308117	−0.154059	+	0.988062i	$0.549235\pi$
$830$	8.48781	0.294616
$831$	30.1936	1.04741
$832$	0	0
$833$	1.80194	0.0624334
$834$	−2.63433	−0.0912194
$835$	−43.3856	−1.50142
$836$	−8.89213	−0.307541
$837$	2.72294	0.0941185
$838$	−0.255356	−0.00882112
$839$	1.78656	0.0616789	0.0308394	−	0.999524i	$-0.490182\pi$
$839$	1.78656	0.0616789	0.0308394	+	0.999524i	$0.490182\pi$
$840$	−2.41496	−0.0833240
$841$	9.72852	0.335466
$842$	−36.2298	−1.24856
$843$	20.4356	0.703839
$844$	−15.6160	−0.537525
$845$	0	0
$846$	9.77289	0.335999
$847$	−0.457123	−0.0157069
$848$	−10.3747	−0.356268
$849$	−4.01876	−0.137923
$850$	1.49925	0.0514239
$851$	−58.8183	−2.01626
$852$	−1.50961	−0.0517183
$853$	−33.5043	−1.14716	−0.573582	−	0.819148i	$-0.694447\pi$
$853$	−33.5043	−1.14716	−0.573582	+	0.819148i	$0.694447\pi$
$854$	6.94297	0.237584
$855$	6.61356	0.226179
$856$	−0.125781	−0.00429909
$857$	−1.66717	−0.0569496	−0.0284748	−	0.999595i	$-0.509065\pi$
$857$	−1.66717	−0.0569496	−0.0284748	+	0.999595i	$0.509065\pi$
$858$	0	0
$859$	2.42584	0.0827685	0.0413842	−	0.999143i	$-0.486823\pi$
$859$	2.42584	0.0827685	0.0413842	+	0.999143i	$0.486823\pi$
$860$	9.54686	0.325545
$861$	9.15862	0.312125
$862$	26.6462	0.907574
$863$	−25.5617	−0.870132	−0.435066	−	0.900399i	$-0.643275\pi$
$863$	−25.5617	−0.870132	−0.435066	+	0.900399i	$0.643275\pi$
$864$	1.00000	0.0340207
$865$	17.4199	0.592293
$866$	−30.6061	−1.04004
$867$	−13.7530	−0.467077
$868$	2.72294	0.0924225
$869$	−7.84967	−0.266282
$870$	−15.0288	−0.509525
$871$	0	0
$872$	3.84276	0.130132
$873$	12.2904	0.415967
$874$	18.0202	0.609543
$875$	10.0655	0.340276
$876$	−0.786291	−0.0265663
$877$	−5.50129	−0.185765	−0.0928827	−	0.995677i	$-0.529608\pi$
$877$	−5.50129	−0.185765	−0.0928827	+	0.995677i	$0.529608\pi$
$878$	−11.4091	−0.385037
$879$	19.3490	0.652627
$880$	−7.84132	−0.264331
$881$	−54.5279	−1.83709	−0.918546	−	0.395313i	$-0.870636\pi$
$881$	−54.5279	−1.83709	−0.918546	+	0.395313i	$0.870636\pi$
$882$	1.00000	0.0336718
$883$	−29.0931	−0.979062	−0.489531	−	0.871986i	$-0.662832\pi$
$883$	−29.0931	−0.979062	−0.489531	+	0.871986i	$0.662832\pi$
$884$	0	0
$885$	10.8675	0.365306
$886$	38.5387	1.29473
$887$	0.0869906	0.00292086	0.00146043	−	0.999999i	$-0.499535\pi$
$887$	0.0869906	0.00292086	0.00146043	+	0.999999i	$0.499535\pi$
$888$	8.93878	0.299966
$889$	−11.7970	−0.395659
$890$	−26.4101	−0.885270
$891$	3.24698	0.108778
$892$	5.53203	0.185226
$893$	−26.7639	−0.895619
$894$	−19.3553	−0.647339
$895$	−7.91848	−0.264686
$896$	1.00000	0.0334077
$897$	0	0
$898$	−2.16519	−0.0722533
$899$	16.9454	0.565162
$900$	0.832022	0.0277341
$901$	−18.6945	−0.622805
$902$	29.7378	0.990162
$903$	−3.95322	−0.131555
$904$	12.7648	0.424552
$905$	−50.7362	−1.68653
$906$	9.50760	0.315869
$907$	20.4983	0.680634	0.340317	−	0.940311i	$-0.389466\pi$
$907$	20.4983	0.680634	0.340317	+	0.940311i	$0.389466\pi$
$908$	20.4532	0.678763
$909$	15.5746	0.516577
$910$	0	0
$911$	31.1649	1.03254	0.516269	−	0.856426i	$-0.327320\pi$
$911$	31.1649	1.03254	0.516269	+	0.856426i	$0.327320\pi$
$912$	−2.73858	−0.0906836
$913$	−11.4121	−0.377685
$914$	−31.4845	−1.04142
$915$	−16.7670	−0.554300
$916$	−29.0317	−0.959234
$917$	−16.5193	−0.545515
$918$	1.80194	0.0594728
$919$	−39.9574	−1.31807	−0.659037	−	0.752110i	$-0.729036\pi$
$919$	−39.9574	−1.31807	−0.659037	+	0.752110i	$0.729036\pi$
$920$	15.8907	0.523901
$921$	5.04050	0.166090
$922$	7.94726	0.261729
$923$	0	0
$924$	3.24698	0.106818
$925$	7.43726	0.244536
$926$	12.1131	0.398061
$927$	3.71813	0.122119
$928$	6.22322	0.204287
$929$	12.8743	0.422393	0.211196	−	0.977444i	$-0.432264\pi$
$929$	12.8743	0.422393	0.211196	+	0.977444i	$0.432264\pi$
$930$	−6.57578	−0.215628
$931$	−2.73858	−0.0897535
$932$	12.4742	0.408605
$933$	−16.2638	−0.532452
$934$	−1.69520	−0.0554687
$935$	−14.1296	−0.462086
$936$	0	0
$937$	−14.9053	−0.486936	−0.243468	−	0.969909i	$-0.578285\pi$
$937$	−14.9053	−0.486936	−0.243468	+	0.969909i	$0.578285\pi$
$938$	−2.54486	−0.0830927
$939$	−8.80560	−0.287360
$940$	−23.6011	−0.769784
$941$	−41.7852	−1.36216	−0.681080	−	0.732209i	$-0.738489\pi$
$941$	−41.7852	−1.36216	−0.681080	+	0.732209i	$0.738489\pi$
$942$	2.70530	0.0881436
$943$	−60.2648	−1.96249
$944$	−4.50007	−0.146465
$945$	−2.41496	−0.0785586
$946$	−12.8360	−0.417335
$947$	−21.9153	−0.712151	−0.356076	−	0.934457i	$-0.615885\pi$
$947$	−21.9153	−0.712151	−0.356076	+	0.934457i	$0.615885\pi$
$948$	−2.41753	−0.0785177
$949$	0	0
$950$	−2.27856	−0.0739263
$951$	20.0495	0.650151
$952$	1.80194	0.0584011
$953$	31.7129	1.02728	0.513641	−	0.858005i	$-0.328296\pi$
$953$	31.7129	1.02728	0.513641	+	0.858005i	$0.328296\pi$
$954$	−10.3747	−0.335893
$955$	14.8590	0.480826
$956$	−23.3225	−0.754303
$957$	20.2067	0.653189
$958$	3.59340	0.116097
$959$	11.5650	0.373455
$960$	−2.41496	−0.0779424
$961$	−23.5856	−0.760826
$962$	0	0
$963$	−0.125781	−0.00405322
$964$	28.8105	0.927922
$965$	44.9743	1.44777
$966$	−6.58012	−0.211712
$967$	9.95706	0.320198	0.160099	−	0.987101i	$-0.448819\pi$
$967$	9.95706	0.320198	0.160099	+	0.987101i	$0.448819\pi$
$968$	−0.457123	−0.0146925
$969$	−4.93476	−0.158527
$970$	−29.6808	−0.952992
$971$	−7.29014	−0.233952	−0.116976	−	0.993135i	$-0.537320\pi$
$971$	−7.29014	−0.233952	−0.116976	+	0.993135i	$0.537320\pi$
$972$	1.00000	0.0320750
$973$	−2.63433	−0.0844527
$974$	−4.79109	−0.153516
$975$	0	0
$976$	6.94297	0.222239
$977$	−15.2936	−0.489285	−0.244643	−	0.969613i	$-0.578671\pi$
$977$	−15.2936	−0.489285	−0.244643	+	0.969613i	$0.578671\pi$
$978$	−6.79361	−0.217236
$979$	35.5092	1.13488
$980$	−2.41496	−0.0771430
$981$	3.84276	0.122690
$982$	−42.3139	−1.35029
$983$	−53.3268	−1.70086	−0.850430	−	0.526089i	$-0.823658\pi$
$983$	−53.3268	−1.70086	−0.850430	+	0.526089i	$0.823658\pi$
$984$	9.15862	0.291966
$985$	−40.7047	−1.29696
$986$	11.2139	0.357122
$987$	9.77289	0.311075
$988$	0	0
$989$	26.0127	0.827155
$990$	−7.84132	−0.249213
$991$	31.4834	1.00010	0.500051	−	0.865996i	$-0.333314\pi$
$991$	31.4834	1.00010	0.500051	+	0.865996i	$0.333314\pi$
$992$	2.72294	0.0864533
$993$	−19.0732	−0.605271
$994$	−1.50961	−0.0478818
$995$	−29.7948	−0.944558
$996$	−3.51468	−0.111367
$997$	−16.4135	−0.519819	−0.259910	−	0.965633i	$-0.583693\pi$
$997$	−16.4135	−0.519819	−0.259910	+	0.965633i	$0.583693\pi$
$998$	26.4820	0.838274
$999$	8.93878	0.282811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.ct.1.1	yes	6
13.12	even	2		7098.2.a.cr.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cr.1.6	✓	6	13.12	even	2
7098.2.a.ct.1.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.41496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} +1.00000 q^{18} -2.73858 q^{19} -2.41496 q^{20} +1.00000 q^{21} +3.24698 q^{22} -6.58012 q^{23} +1.00000 q^{24} +0.832022 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.22322 q^{29} -2.41496 q^{30} +2.72294 q^{31} +1.00000 q^{32} +3.24698 q^{33} +1.80194 q^{34} -2.41496 q^{35} +1.00000 q^{36} +8.93878 q^{37} -2.73858 q^{38} -2.41496 q^{40} +9.15862 q^{41} +1.00000 q^{42} -3.95322 q^{43} +3.24698 q^{44} -2.41496 q^{45} -6.58012 q^{46} +9.77289 q^{47} +1.00000 q^{48} +1.00000 q^{49} +0.832022 q^{50} +1.80194 q^{51} -10.3747 q^{53} +1.00000 q^{54} -7.84132 q^{55} +1.00000 q^{56} -2.73858 q^{57} +6.22322 q^{58} -4.50007 q^{59} -2.41496 q^{60} +6.94297 q^{61} +2.72294 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} -2.54486 q^{67} +1.80194 q^{68} -6.58012 q^{69} -2.41496 q^{70} -1.50961 q^{71} +1.00000 q^{72} -0.786291 q^{73} +8.93878 q^{74} +0.832022 q^{75} -2.73858 q^{76} +3.24698 q^{77} -2.41753 q^{79} -2.41496 q^{80} +1.00000 q^{81} +9.15862 q^{82} -3.51468 q^{83} +1.00000 q^{84} -4.35160 q^{85} -3.95322 q^{86} +6.22322 q^{87} +3.24698 q^{88} +10.9361 q^{89} -2.41496 q^{90} -6.58012 q^{92} +2.72294 q^{93} +9.77289 q^{94} +6.61356 q^{95} +1.00000 q^{96} +12.2904 q^{97} +1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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